# 4.1 Multiple plant, product and period models

The purpose of this section is to show how large linear programming (LP) models can arise through the combining of smaller models. Almost all very large models arise in this way. Such models prove to be more powerful as decision making tools than the submodels from which they are constructed. In order to illustrate how a multiplant model can arise in this way, we take a very small illustrative example.

Example 4.1: A Multiplant Model
A company operates in two factories, A and B. Each factory makes two products, standard and deluxe. A unit of standard gives a profit contribution of £10, while a unit of deluxe gives a profit contribution of £15.
Each factory uses two processes, grinding and polishing, for producing its products. Factory A has a grinding capacity of 80 hours per week and polishing capacity of 60 hours per week. For factory B, these capacities are 60 and 75 hours per week, respectively.
The grinding and polishing times in hours for a unit of each type of product in each factory are given in the table below.
It is possible, for example, that factory B has older machines than factory A, resulting in higher unit processing times.
In addition, each unit of each product uses 4 kg of a raw material, which we refer to as raw. The company has 120 kg of raw available per week. To start ...

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